Duality of causal distributionally robust optimization
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911179835703296 |
|---|---|
| author | Jiang, Yifan |
| author_facet | Jiang, Yifan |
| contents | We study the distributionally robust optimization (DRO) in a dynamic context where the model uncertainty is captured by penalizing potential models in function of their adapted Wasserstein distance to a given reference model. We consider both discrete- and continuous-time settings and derive dynamic duality formulas that reformulate the worst-case expectation as a tractable minimax problem. The inner maximum can be computed recursively in discrete time, or solved by a path-dependent Hamilton--Jacobi--Bellman equation in continuous time. We further extend these duality results from the worst-case expectation to the worst-case expected shortfall, a non-linear expectation. Finally, we apply the DRO framework to optimal stopping problems in discrete time. We recast the original problem as a classical Wasserstein DRO on a nested space by introducing a novel relaxation that considers stopping times with respect to general flitrations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16556 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Duality of causal distributionally robust optimization Jiang, Yifan Probability Optimization and Control 60G40, 90C46, 93E03 We study the distributionally robust optimization (DRO) in a dynamic context where the model uncertainty is captured by penalizing potential models in function of their adapted Wasserstein distance to a given reference model. We consider both discrete- and continuous-time settings and derive dynamic duality formulas that reformulate the worst-case expectation as a tractable minimax problem. The inner maximum can be computed recursively in discrete time, or solved by a path-dependent Hamilton--Jacobi--Bellman equation in continuous time. We further extend these duality results from the worst-case expectation to the worst-case expected shortfall, a non-linear expectation. Finally, we apply the DRO framework to optimal stopping problems in discrete time. We recast the original problem as a classical Wasserstein DRO on a nested space by introducing a novel relaxation that considers stopping times with respect to general flitrations. |
| title | Duality of causal distributionally robust optimization |
| topic | Probability Optimization and Control 60G40, 90C46, 93E03 |
| url | https://arxiv.org/abs/2401.16556 |